For many people mathematics is something like a very huge and impressive building. It has a given structure with lots of levels and rooms. For many people this structure and therefore mathematics itself is independent from society, culture and history. It exists and mathematicians try to recover (not: to construct!) new parts of it. From this point of view mathematics is often seen as a lifeless and strange thing and not as a living construct of human beings. Many mathematics teachers argue that they can't change their way of teaching because they see mathematics from this dominant point of view and think that mathematics will not allow changes. Asking what this means they say that mathematics is something independent from them with a fixed structure. Therefore they have to teach little parts of mathematics (often concentrated on the correct use of algorithms) in a fixed sequence. Changing the sequence or leaving out a part seems to be not allowed. So they are not happy with mathematics but they see no way to change mathematics and therefore no way to change their teaching (perhaps except in some minor important methodical aspects). I think there is a "way out" if mathematics is seen as a social construct. Is this view correct? A new look at the history of mathematics proves that the history of mathematics in the last 200 years looks like a very good example of applying a sociological theory to make a new interpretation of what happens. In more provocative words: If the sociological theory I apply to make my interpretation of the history of mathematics had existed 200 years ago one could think that the mathematicians tried to prove that the sociological theory is correct by forming the history of mathematics in the way the theory "wants". If teachers try to share this view they will be able to recognize that mathematicians decided what "mathematics" is. I hope this will motivate teachers to make more individual and pedagogical decisions on what and how they teach.